CAIE P1 2018 June — Question 10

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2018
SessionJune
TopicComposite & Inverse Functions

10 The one-one function f is defined by \(\mathrm { f } ( x ) = ( x - 2 ) ^ { 2 } + 2\) for \(x \geqslant c\), where \(c\) is a constant.
  1. State the smallest possible value of \(c\).
    In parts (ii) and (iii) the value of \(c\) is 4 .
  2. Find an expression for \(\mathrm { f } ^ { - 1 } ( x )\) and state the domain of \(\mathrm { f } ^ { - 1 }\).
  3. Solve the equation \(\mathrm { ff } ( x ) = 51\), giving your answer in the form \(a + \sqrt { } b\).